Note. The ale gallon contains 282 cubic or solid inches.* Note. By this are measured all wines, spirits, strong-waters, cider, mead, perry, vinegar, oil, honey, &c. The wine gallon contains 231 cubic or solid inches.* And it is *The ale and wine gallons in England have lately been reduced to one of 277 cubic inches. remarkable, that the wine and ale gallons have the same proportion to each other, as the troy and avoirdupois pounds have; that is, as one pound troy is to one pound avoirdupois, so is one wine gallon to one ale gallon. 2419200 31557600 1 Year 525960 = 8766 = 365 = Wk Da Hr Mo Da Hr Or 52 1 6 = 13 1 6 = 1 Julian Year 100. It is evident, that if the several denominations of money, weight, and measure proceeded in a decimal ratio, the fundamental operations might be performed upon these, as upon abstract numbers. This may be shown by a few examples in Federal Money. If it were required to find the sum of $46,85 and $256,371, we should place the numbers of the same denomination in the same column, and add them together as in whole numbers; thus, 4685 256371 303221 and the answer may be read off in either or all the denominations; we may say 30 eagles 3 dollars 22 cents 1 mill, or 303 dollars 221 thousandths, or 30322 cents and 1 tenth, or 303221 mills. It is usual to consider the dollars as whole numbers, and the following denominations as decimals. The operation then becomes the same as for decimals. 101. When the different denominations do not proceed in a decimal ratio, they may all be reduced to one denomination, and then the fundamental operations may be performed upon this, as upon an abstract number. If, for example, the sum to be operated upon were £4. 15s. 9d. this may easily be expressed in pence. As 1 pound is 20 shillings, 4 pounds will be 4 times 20, or 80 shillings. If to this we add the 15s. we shall have 95s. 9d. equivalent to the above. But as 1 shilling is equal to 12 pence, 95s. will be equal to 95 times 12, or 1140 pence. Adding 9 to this, we shall have 1149 pence as an equivalent expression for £4. 15s. 9d. We may now make use of this number as if it had no relation to money or any thing else; and the result obtained may be converted again into the different denominations by reversing the process above pursued. If it were proposed to multiply this sum by another nnmber, 37 for instance, we should find the product of these two numbers in the usual way; thus, 1149 37 8043 3447 42513 42513 is, therefore, equal to 37 times £4. 15s. 9d. expressed in pence: to find the number of pounds and shillings contained in this, we first obtain the number of shillings by dividing it by 12, which gives 3542, and then the number of pounds by dividing this last by 20; thus, 42513 pence then is equal to 3542 shillings and 9 pence, or to 177 pounds 2 shillings and 9 pence. Whence 37 times £4. 15s. 9d. is equal to £177. 2s. 9d. It may be remarked, that shillings are converted into pounds by separating the right hand figure and dividing those on the left by 2, prefixing the remainder, if there be one, to the figure separated for the entire shillings, that remain. This amounts to dividing, first, by 10 (90), and then that quotient by 2. If 10 shillings made a pound, dividing by 10 would give the number of pounds, but as 10 shillings are only half a pound, half this number will be the number of pounds. By a method similar to that above given, we reduce other denominations of money and the different denominations of the several weights and measures to the lowest respectively. If it were required to find how many grains there are in 2lb. 4oz. 17dwt. 5grs. Troy, we should proceed thus, |